Step 1: Determine If you qualify for Verified Twitter account by reading Twitter Terms & ConditionsStep 2: Put a Twitter Follow account on your websiteStep 3: Contact Twitter by filling up the formRequest to verify an accountStep 3: Submit the form by entering your Twitter Username and PasswordSUBMIT FORM

Be sure to have the following information ready:1. Account name2. Full name3. Location4. Official website (you will be given a suggestion to put the Twitter logo or badge on your official website to speed up verification)5. Bio information (your 160 character profile summary)6. Primary contact name (you or the individual who manages the account)7. Additional contact information

Step 4: Once you send the complete information as mentioned above. Twitter Support will contact you immediately

The link doesn't show me a form.
EDIT: I believe this is an outdated method, because Twitter used to have a Form to submit profile verification badge requests, but they closed it for the public. So, only a limited number of people have access to such a form now!